Abstract:
In this study, we focus on finding the possible optimal strategy where there is consump tion, stochastic income, purchasing of life insurance and investment in risky and risk-less
investments are made. The stock follows a jump diffusion process and the bond is linked to
inflation making the two risky and we have the investment position taken also on the money
market account. The wealth process is determined by the different generations of the life of
an investor, that is before the investor dies and after the investor dies. We also look into the
optimal portfolio the beneficiaries benefit after the investor dies. We applied the concept of
change of probability measures considering the Girsanov’s and the Radon-Nikodym the orems, we found the generator of the Backward Stochastic differential equations defined
and employed the Hamilton-Jacobi-Bellman dynamic programming (HJB) in finding the
stochastic optimal controls of interest. The optimal strategies are explicitly obtained.
Sophie, M (2024). Optimal Investment-consumption-insurance strategy with inflation risk and stochastic income in an Ito-levy setting. Afribary. Retrieved from https://afribary.com/works/optimal-investment-consumption-insurance-strategy-with-inflation-risk-and-stochastic-income-in-an-ito-levy-setting
Sophie, Moagi "Optimal Investment-consumption-insurance strategy with inflation risk and stochastic income in an Ito-levy setting" Afribary. Afribary, 30 Mar. 2024, https://afribary.com/works/optimal-investment-consumption-insurance-strategy-with-inflation-risk-and-stochastic-income-in-an-ito-levy-setting. Accessed 26 Jul. 2024.
Sophie, Moagi . "Optimal Investment-consumption-insurance strategy with inflation risk and stochastic income in an Ito-levy setting". Afribary, Afribary, 30 Mar. 2024. Web. 26 Jul. 2024. < https://afribary.com/works/optimal-investment-consumption-insurance-strategy-with-inflation-risk-and-stochastic-income-in-an-ito-levy-setting >.
Sophie, Moagi . "Optimal Investment-consumption-insurance strategy with inflation risk and stochastic income in an Ito-levy setting" Afribary (2024). Accessed July 26, 2024. https://afribary.com/works/optimal-investment-consumption-insurance-strategy-with-inflation-risk-and-stochastic-income-in-an-ito-levy-setting